'public' is not valid for this item

Solution 1:

You have a nested/local method BirdDied, that can't have access modifiers. It's accessible only from the method body of Update anyway. So this compiles:

void Update ()
{
    void BirdDied()
    {
        GameOverText.SetActive (true);
        gameOver = true;
    }
}

But since you don't use it in your code, i doubt that it's what you want.